G16.3

AIDS-related risk factors. Exercise 16.1 introduced a problem in which a random sample of 2,673 adult heterosexuals were asked about presence of an HIV risk factor.

1. Describe the sampling distribution of the number of individuals who are positive for this risk factor.
2. Do you think a Normal approximation can be used to characterize the sampling distribution? Explain. We can use the Normal distribution to approximate the Binomial when the sample size is sufficiently large relative to the "p". Thanks our 'rule of thumb' we'd need to check np>=10 and n(1-p)>=10.

Unless the unknown p is tiny, with our large sample size of 2673, we can probably use the normal approximation to the binomial.